Algebraic Topology Special Session, BMC 2007

Infinite dimensional Riemannian manifolds have traditionally been divided into two types: strong and weak. One can generalise many of the standard constructions of Riemannian geometry to strong Riemannian manifolds but not to weak ones. In this talk I shall examine some of the basic results of Riemannian geometry in order to refine this classification. The purpose is to show that some constructions can be generalised to certain weak Riemannian manifolds. I shall conclude by describing which level of structure is available for the free loop space of a finite dimensional manifold and by explaining how this can be used in applications.

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This talk was given as a beamer presentation. You can download various versions of it together with the source files. The best version for the content of the talk is the article one.

• Presentation version in pdf. This was what was actually shown on the screen.
• Slides version in pdf. This was the backup version for an OHP in case of computer failure. For the most part, it is a one slide per frame version of the presentation though there is one frame still with overlays.
• Article in pdf. This is a reasonably readable version of what I said (or rather, what I intended to say).
• Notes in pdf. These are the notes that I printed out to help me remember what to say (I actually printed these out 4-up).
• Source as a tarball. All of the above versions have the same basic source file and are produced by invoking the beamer class in slightly different ways. The method I use of doing this is having header files which set things up and then input the main file. The main file is geometry.tex and the others are geometry.something.tex.